NCERT 5th Class (CBSE) Mathematics: Introduction To Algebra

We know that a mathematical expression uses mathematical symbols instead of words. For example, the words ‘twenty-eight increased by five’, will be shown as the mathematical expression 28 + 5.

Can you give the mathematical expressions for these words?

1. Seventy three minus forty -two
2. Twelve less two
3. Six times fifteen
4. Thirty plus eleven take away nine

Sometimes, in a mathematical expression, we use letters to represent numbers we do not know.

If we say that there were some people at a party and 7 people left, we can show this as an expression, n-7, where n represents the number of people in the party.

If there were 12 people at the party, then n would represent 12. If there were 20 people at the party, then n would represent 20.

These letters are called variable because they can represent any number.

CHECKPOINT: When we write an expression using variables, words and/or operations, it is called an algebraic expression.

Let p be the number of pencils in your pencil box. Study the algebraic expressions for each:

12 pencils more than the number of pencils in your box → p + 12 or 12 + p

4 pencils less than the number of pencils in your box → p – 4

Three times the number of pencils in your box.  → 3 × p also written as 3p

The number of pencils in your box divided by 4  → p ÷ 4 also written as p/4

Here, the expressions have been put into words. The unknown number or the variable is w.

18 + w → w added to 18

10 – w → w subtracted from 10

7w → The product of w and 7

6 ÷ w → 6 divided by w

If we know that w = 3, Then expressions above can be simplified and a value can be obtained for each expression.

If we substitute 3 in place of w, we get

18 + w = 18 + 3 = 21

10 – w = 10 – 3 = 7

7w = 7 × 3 = 21

6 ÷ w = 6 ÷ 3 = 2